Monty Hall Simulation Calculator
ActualMontyHallsimulationinformedhostalwaysopensgoat,uniformeligible door,explicitalwaysswitchpolicy;no genericuninformedhost variant. Boundedoffline arithmetic/sampling only;not gambling advice,fair physical randomness,secure randomness or predictive certainty.
Description
The Monty Hall model depends on an informed host who always reveals a goat and offers the remaining door.
The Monty Hall model depends on an informed host who always reveals a goat and offers the remaining door.1
This simulation uses that host rule and an explicit always-switch policy.
When to use Monty Hall Simulation Calculator
Use this tool to apply the stated monty hall simulation calculator operation with an explicit input and unit basis.
How to use Monty Hall Simulation Calculator and how it works
- Establish the text or game convention described above.
- Enter seed, trialCount, alwaysSwitch and run the tool.
- Read result.wins, result.trials, result.observedWinFraction using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| seed | Nonblank reproducibility string, at most 256 characters; required even with a supplied random source. | string | required; further conditions in the algorithm |
| trialCount | Trial count, on the basis specified in the algorithm. | number | required; finite; integer from 1 to 10000; further conditions in the algorithm |
| alwaysSwitch | Always switch, on the basis specified in the algorithm. | boolean | required; further conditions in the algorithm |
Require integer trials 1–10,000. Draw prize and initial door, uniformly choose an eligible goat door, apply switch or stay, and count wins; return trials and observed win fraction. A nonblank seed of at most 256 characters selects the existing seeded generator unless execution context supplies random. One source advances through the request; supplied samples must be finite in [0,1). These draws are not cryptographically secure.
The default source hashes the seed’s UTF-16 units into an integer state and advances a deterministic arithmetic generator for each sample. A supplied execution-context random source takes precedence; it must return finite values in [0,1). The required seed still must be nonblank and at most 256 characters. These draws are reproducible entertainment or sampling, without cryptographic unpredictability.2
observed fraction = wins/trials under informed-host policy Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.wins | Number of simulated winning trials. | number |
| result.trials | Supplied simulation trial count. | number |
| result.observedWinFraction | Wins divided by trials, a sampled fraction rather than an exact theoretical probability. | number |
{
"input": {
"seed": "batch51",
"trialCount": 2,
"alwaysSwitch": true
},
"output": {
"result": {
"wins": 1,
"trials": 2,
"observedWinFraction": 0.5
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A successful false boolean, negative signed difference, empty slice or unresolved tie is distinct from an input error. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Scratch Card Odds Calculator. Remaining-ticket odds require verified counts on the same sold-or-unsold basis.
For a related operation, use Rock Paper Scissors Lizard Spock Advisor. Rock-paper-scissors-lizard-Spock can use a uniformly drawn move for casual play.
References
-
Monty Hall Simulation Calculator — tool.io
-
Existing seeded random generator — tool.io
Similar or alternative tools
- Scratch Card Odds Calculator
Remaining-ticket odds require verified counts on the same sold-or-unsold basis.
- Rock Paper Scissors Lizard Spock Advisor
Rock-paper-scissors-lizard-Spock can use a uniformly drawn move for casual play.